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These results may seem paradoxical. Is not a birth prevented in a birth control program a reduction of one in the population of the immediate future irrespective of the age of the mother who is persuaded not to have a child? It is, but one judges the success of a continuing birth control program on the degree to which it creates a downtrend in age-specific rates, and the effect of this downtrend on the long-run rate of growth of the population.
The above analysis is concerned with age-specific birth rates, and these are but one mode of analysis. Insofar as there are more women in a population at younger ages, the effort required to lower the age-specific rate Fx would have to be greater for younger than for older women. Moreover, insofar as older women are more willing to protect themselves against further population increase less effort of persuasion is required to bring each one into the program than to bring in a younger woman. On the other hand, insofar as older women are less fertile when unprotected and more likely to resort on their own initiative to traditional methods of birth control, the impact on population increase of each induction of a woman of 40 into modern methods would be relatively less than that of a woman of 20. A rich literature on the probability aspects of contraception is now coming into existence, the main contributors being Mindel C. Sheps and Robert J. Potter, Jr. [See, for example (5, 6).]
Departures from Stability
In using the stable model we have been taking advantage of the extent to which the observed population is approximated by the stable. But the same parameters, and in particular the intrinsic rates of birth and death, enable us to study also the nature of departures from stability.
The characteristics of a population that would result from persistence of its regime of mortality and fertility have been called intrinsic; from r, the intrinsic rate of natural increase, we obtain b, the intrinsic birth rate and d, the intrinsic death rate. All of these may be very different from the observed rates in a population that controls its births to make them accord with the fluctuations of the economy. In 1966 the observed crude death rate of United States females was 8.11 per thousand; if the 1966 age-specific rates of birth and death persisted the crude death rate would steadily increase-to 8.72 in 1971, to 9.06 in 1976, and ultimately to 9.60. The ultimate or intrinsic death rate will be higher than the rate presently observed because the population will be older. This aging arises partly from the improved mortality now in effect gradually leading to an older population and partly from a lower birth rate in the present than in the past.
On the same assumptions, the U.S. female birth rate will move up from 17.61 per 1,000 to 19.30. The reason is that persistence of the 1966 regime would increase the proportion of women of childbearing age in the popula-tainment of Educa-bout 20 percent. For the less developedHilton Salhanick has observed that some women practicing the rhythm method will break or lose their thermometers at the critical juncture in theirright, therefore alwayshas some c